In recent years, the world has witnessed explosive growth in the demand for wireless communications and it is predicted that this demand will increase in the future. There are already over 500 million users that subscribe to cellular telephone services and the number is continually increasing. Eventually, in the not too distant future the number of cellular subscribers will exceed the number of fixed line telephone installations. Already, in many cases, the revenues from mobile services exceeds that for fixed line services even though the amount of traffic generated through mobile phones is much less than in fixed networks.
Other related wireless technologies have experienced growth similar to that of cellular. For example, cordless telephony, two way radio trunking systems, paging (one way and two way), messaging, wireless local area networks (WLANs) and wireless local loops (WLLs). In addition, new broadband communication schemes are rapidly being deployed to provide users with increased bandwidth and faster access to the Internet. Broadband services such as xDSL, short range high speed wireless connections, high rate satellite downlink (and the uplink in some cases) are being offered to users in more and more locations.
In connection with cellular services, the majority of users currently subscribe to digital cellular networks. Almost all new cellular handsets sold to customers are based on digital technology, typically second generation digital technology. Currently, third generation digital networks are being designed, developed and tested which will be able to support data packet networks having much higher data rates. The first generation analog systems comprise the well known protocols Advanced Mobile Telephone System (AMPS), Total Access Communications Systems (TACS), etc. The digital systems comprise Global System for Mobile Communication (GSM), GSM EDGE Radio Access Network (GERAN), Time Division Multiple Access (TDMA) (IS-136) or Code Division Multiple Access (CDMA) (IS-95), for example.
Communications receivers such as modems designed for wireless channels employ equalizers to combat the intersymbol interference caused by the time dispersion of the channel. Wireless channels can be characterized as time dispersive, frequency selective fading channels. The characteristics of such channels may change significantly during transmission of a message, in the case of GSM, during an Enhanced General Packet Radio System EGPRS burst. Optimum performance cannot be achieved without tracking such a channel during the burst. Therefore, many systems employ some form of channel tracking which is operative to update the channel model during each burst in order to achieve better performance.
Several adaptive type algorithms are commonly used for channel tracking in wireless modems. These algorithms are used to periodically update the channel estimate during the burst. The most common algorithms include least means squares (LMS) and recursive least squares (RLS). RLS based algorithms are known to have better convergence properties and are asymptotically optimal. The good convergence properties of the RLS algorithm is due to the use of information contained in the input data extending back to the instant of time when the algorithm was initiated. The recursive least squares algorithm starts with known initial conditions while using the information contained in new data samples to update old estimates. The resulting rate of convergence is usually an order of magnitude faster than the LMS algorithm. The improvement, however, is achieved at the expense of an increase in computational complexity over the LMS algorithm.
Although the RLS algorithm has good tracking and convergence properties, a disadvantage is that its use of a relation in matrix algebra known as the matrix inversion lemma causes numerical problems when implemented on fixed-point processors. The finite precision of fixed-point digital signal processors makes such an algorithm difficult to implement.
Another disadvantage is that prior art RLS based tracking algorithms, provide channel updates every sample time thus precluding the use of precalculated tables in the equalizer. This significantly increases the complexity of the equalizer due to the requirement of repeatedly performing convolution calculations for each sample. Normally, the results of the convolution between the samples and the channel estimate, for example, are precalculated and stored in a table within the equalizer since the same calculations need to be performed many times in computing branch metrics while traversing the trellis (such as in RSSE type equalizers).
Moreover, Viterbi type equalizers provide decisions only at the end of the burst after processing the last input sample. Conventional RLS algorithms, however, require decisions each sample. This increases the overhead of the decision generation process and decreases the reliability of the decisions.
It is therefore desirable to provide a mechanism for tracking changes to the channel during a burst that provides good tracking abilities, has good convergence properties, is numerically stable and does not increase the complexity of the equalizer.